SymEngine::Rational Class Reference

Rational Class. More...

#include <rational.h>

Inheritance diagram for SymEngine::Rational:

Collaboration diagram for SymEngine::Rational:

Public Member Functions
void	accept (Visitor &v) const override
void	accept (EvalRealDoubleVisitorFinal &v) const override
	Rational (rational_class &&_i)
	Constructor of Rational class.
hash_t	__hash__ () const override
bool	__eq__ (const Basic &o) const override
int	compare (const Basic &o) const override
bool	is_canonical (const rational_class &i) const
const rational_class &	as_rational_class () const
	Convert to rational_class.
bool	is_zero () const override
bool	is_one () const override
bool	is_minus_one () const override
bool	is_int () const
bool	is_positive () const override
bool	is_negative () const override
bool	is_complex () const override
RCP< const Rational >	neg () const
bool	is_perfect_power (bool is_expected=false) const override
bool	nth_root (const Ptr< RCP< const Number >> &, unsigned long n) const override
RCP< const Number >	addrat (const Rational &other) const
RCP< const Number >	addrat (const Integer &other) const
RCP< const Number >	subrat (const Rational &other) const
RCP< const Number >	subrat (const Integer &other) const
RCP< const Number >	rsubrat (const Integer &other) const
RCP< const Number >	mulrat (const Rational &other) const
RCP< const Number >	mulrat (const Integer &other) const
RCP< const Number >	divrat (const Rational &other) const
RCP< const Number >	divrat (const Integer &other) const
RCP< const Number >	rdivrat (const Integer &other) const
RCP< const Number >	powrat (const Integer &other) const
RCP< const Basic >	powrat (const Rational &other) const
RCP< const Basic >	rpowrat (const Integer &other) const
RCP< const Number >	add (const Number &other) const override
	Converts the param other appropriately and then calls addrat
RCP< const Number >	sub (const Number &other) const override
	Converts the param other appropriately and then calls subrat
RCP< const Number >	rsub (const Number &other) const override
	Converts the param other appropriately and then calls rsubrat
RCP< const Number >	mul (const Number &other) const override
	Converts the param other appropriately and then calls mulrat
RCP< const Number >	div (const Number &other) const override
	Converts the param other appropriately and then calls divrat
RCP< const Number >	rdiv (const Number &other) const override
	Converts the param other appropriately and then calls rdivrat
RCP< const Number >	pow (const Number &other) const override
	Converts the param other appropriately and then calls powrat
RCP< const Number >	rpow (const Number &other) const override
RCP< const Integer >	get_num () const
RCP< const Integer >	get_den () const
Public Member Functions inherited from SymEngine::Number
virtual RCP< const Basic >	conjugate () const
virtual bool	is_exact () const
	return true if the number is an exact representation
bool	is_exact_zero () const
virtual Evaluate &	get_eval () const
	Get Evaluate singleton to evaluate numerically.
vec_basic	get_args () const override
	Returns the list of arguments.
Public Member Functions inherited from SymEngine::Basic
TypeID	get_type_code () const
	Basic ()
	Constructor.
	Basic (const Basic &)=delete
	Delete the copy constructor and assignment.
Basic &	operator= (const Basic &)=delete
	Assignment operator in continuation with above.
	Basic (Basic &&)=delete
	Delete the move constructor and assignment.
Basic &	operator= (Basic &&)=delete
	Assignment operator in continuation with above.
hash_t	hash () const
bool	__neq__ (const Basic &o) const
	true if this is not equal to o. More...
int	__cmp__ (const Basic &o) const
	Comparison operator.
std::string	__str__ () const
std::string	dumps () const
	Returns a string of the instance serialized.
RCP< const Basic >	subs (const map_basic_basic &subs_dict) const
	Substitutes 'subs_dict' into 'self'.
RCP< const Basic >	xreplace (const map_basic_basic &subs_dict) const
virtual RCP< const Basic >	expand_as_exp () const
	expands the special function in terms of exp function
RCP< const Basic >	diff (const RCP< const Symbol > &x, bool cache=true) const
Public Member Functions inherited from SymEngine::EnableRCPFromThis< Basic >
RCP< Basic >	rcp_from_this ()
	Get RCP<T> pointer to self (it will cast the pointer to T)
RCP< const Basic >	rcp_from_this () const
	Get RCP<const T> pointer to self (it will cast the pointer to const T)
RCP< const T2 >	rcp_from_this_cast () const
	Get RCP<T2> pointer to self (it will cast the pointer to T2)
unsigned int	use_count () const

Static Public Member Functions
static RCP< const Number >	from_mpq (const rational_class &i)
static RCP< const Number >	from_mpq (rational_class &&i)
static RCP< const Number >	from_two_ints (const Integer &n, const Integer &d)
static RCP< const Number >	from_two_ints (const long n, const long d)
Static Public Member Functions inherited from SymEngine::Basic
static RCP< const Basic >	loads (const std::string &)
	Creates an instance of a serialized string.

Static Public Attributes
static const TypeID	type_code_id = SYMENGINE_RATIONAL

Private Attributes
rational_class	i
	i : object of rational_class

Additional Inherited Members
Data Fields inherited from SymEngine::Basic
TypeID	type_code_

Detailed Description

Rational Class.

Definition at line 15 of file rational.h.

Member Function Documentation

__eq__()

bool SymEngine::Rational::__eq__ ( const Basic &  o ) const

overridevirtual

Equality comparator

Parameters

o	- Object to be compared with

Returns

whether the 2 objects are equal

Implements SymEngine::Basic.

Definition at line 106 of file rational.cpp.

{
    if (is_a<Rational>(o)) {
        const Rational &s = down_cast<const Rational &>(o);
        return this->i == s.i;
    }
    return false;
}

Code

__hash__()

hash_t SymEngine::Rational::__hash__ ( ) const

overridevirtual

Returns

size of the hash

Implements SymEngine::Basic.

Definition at line 96 of file rational.cpp.

{
    // only the least significant bits that fit into "signed long int" are
    // hashed:
    hash_t seed = SYMENGINE_RATIONAL;
    hash_combine<long long int>(seed, mp_get_si(SymEngine::get_num(this->i)));
    hash_combine<long long int>(seed, mp_get_si(SymEngine::get_den(this->i)));
    return seed;
}

Code

addrat() [1/2]

RCP<const Number> SymEngine::Rational::addrat ( const Integer &  other ) const

inline

Add Rationals

Parameters

other

of type Integer

Definition at line 112 of file rational.h.

    {
        return from_mpq(this->i + other.as_integer_class());
    }

Code

addrat() [2/2]

RCP<const Number> SymEngine::Rational::addrat ( const Rational &  other ) const

inline

Add Rationals

Parameters

other

of type Rational

Definition at line 105 of file rational.h.

    {
        return from_mpq(this->i + other.i);
    }

Code

compare()

int SymEngine::Rational::compare ( const Basic &  o ) const

overridevirtual

Returns -1, 0, 1 for this < o, this == o, this > o. This method is used when you want to sort things like x+y+z into canonical order. This function assumes that o is the same type as this. Use __cmp__ if you want general comparison.

Implements SymEngine::Basic.

Definition at line 115 of file rational.cpp.

{
    if (is_a<Rational>(o)) {
        const Rational &s = down_cast<const Rational &>(o);
        if (i == s.i)
            return 0;
        return i < s.i ? -1 : 1;
    }
    if (is_a<Integer>(o)) {
        const Integer &s = down_cast<const Integer &>(o);
        return i < s.as_integer_class() ? -1 : 1;
    }
    throw NotImplementedError("unhandled comparison of Rational");
}

Code

divrat() [1/2]

RCP<const Number> SymEngine::Rational::divrat ( const Integer &  other ) const

inline

Divide Rationals

Parameters

other

of type Integer

Definition at line 166 of file rational.h.

    {
        if (other.as_integer_class() == 0) {
            if (this->i == 0) {
                return Nan;
            } else {
                return ComplexInf;
            }
        } else {
            return from_mpq(this->i / other.as_integer_class());
        }
    }

Code

divrat() [2/2]

RCP<const Number> SymEngine::Rational::divrat ( const Rational &  other ) const

inline

Divide Rationals

Parameters

other

of type Rational

Definition at line 151 of file rational.h.

    {
        if (other.i == 0) {
            if (this->i == 0) {
                return Nan;
            } else {
                return ComplexInf;
            }
        } else {
            return from_mpq(this->i / other.i);
        }
    }

Code

from_mpq()

RCP< const Number > SymEngine::Rational::from_mpq ( const rational_class &  i )

static

Parameters

<tt>i</tt>

must already be in rational_class canonical form

Returns

Integer or Rational depending on denumerator.

Definition at line 23 of file rational.cpp.

{
    // If the result is an Integer, return an Integer:
    if (SymEngine::get_den(i) == 1) {
        return integer(SymEngine::get_num(i));
    } else {
        rational_class j(i);
        return make_rcp<const Rational>(std::move(j));
    }
}

Code

from_two_ints()

RCP< const Number > SymEngine::Rational::from_two_ints ( const Integer &  n, const Integer &  d  )

static

Constructs Rational as n/d, where n, d can be any Integers. If n/d is an Integer, it will return an Integer instead.

Definition at line 44 of file rational.cpp.

{
    if (d.as_integer_class() == 0) {
        if (n.as_integer_class() == 0) {
            return Nan;
        } else {
            return ComplexInf;
        }
    }
#if SYMENGINE_INTEGER_CLASS == SYMENGINE_BOOSTMP
    // workaround https://github.com/boostorg/rational/issues/27
    rational_class q;
    if (d.as_integer_class() < 0) {
        q = rational_class(-n.as_integer_class(), -d.as_integer_class());
    } else {
        q = rational_class(n.as_integer_class(), d.as_integer_class());
    }
#else
    rational_class q(n.as_integer_class(), d.as_integer_class());
#endif
    // This is potentially slow, but has to be done, since 'n/d' might not be
    // in canonical form.
    canonicalize(q);
 
    return Rational::from_mpq(std::move(q));
}

Code

is_canonical()

bool SymEngine::Rational::is_canonical

(

const rational_class &

i

)

const

Returns

true if canonical

Definition at line 8 of file rational.cpp.

{
    rational_class x = i;
    canonicalize(x);
    // If 'x' is an integer, it should not be Rational:
    if (SymEngine::get_den(x) == 1)
        return false;
    // if 'i' is not in canonical form:
    if (SymEngine::get_num(x) != SymEngine::get_num(i))
        return false;
    if (SymEngine::get_den(x) != SymEngine::get_den(i))
        return false;
    return true;
}

Code

is_complex()

bool SymEngine::Rational::is_complex ( ) const

inlineoverridevirtual

Returns

false

Implements SymEngine::Number.

Definition at line 86 of file rational.h.

    {
        return false;
    }

Code

is_int()

bool SymEngine::Rational::is_int ( ) const

inline

Returns

true if denominator is 1

Definition at line 70 of file rational.h.

    {
        return this->i == 1;
    }

Code

is_minus_one()

bool SymEngine::Rational::is_minus_one ( ) const

inlineoverridevirtual

Returns

true if -1

Implements SymEngine::Number.

Definition at line 65 of file rational.h.

    {
        return this->i == -1;
    }

Code

is_negative()

bool SymEngine::Rational::is_negative ( ) const

inlineoverridevirtual

Returns

true if negative

Implements SymEngine::Number.

Definition at line 80 of file rational.h.

    {
        return i < 0;
    }

Code

is_one()

bool SymEngine::Rational::is_one ( ) const

inlineoverridevirtual

Returns

true if 1

Implements SymEngine::Number.

Definition at line 60 of file rational.h.

    {
        return this->i == 1;
    }

Code

is_positive()

bool SymEngine::Rational::is_positive ( ) const

inlineoverridevirtual

Returns

true if positive

Implements SymEngine::Number.

Definition at line 75 of file rational.h.

    {
        return i > 0;
    }

Code

is_zero()

bool SymEngine::Rational::is_zero ( ) const

inlineoverridevirtual

Returns

true if 0

Implements SymEngine::Number.

Definition at line 55 of file rational.h.

    {
        return this->i == 0;
    }

Code

mulrat() [1/2]

RCP<const Number> SymEngine::Rational::mulrat ( const Integer &  other ) const

inline

Multiply Rationals

Parameters

other

of type Integer

Definition at line 144 of file rational.h.

    {
        return from_mpq(this->i * other.as_integer_class());
    }

Code

mulrat() [2/2]

RCP<const Number> SymEngine::Rational::mulrat ( const Rational &  other ) const

inline

Multiply Rationals

Parameters

other

of type Rational

Definition at line 137 of file rational.h.

    {
        return from_mpq(this->i * other.i);
    }

Code

neg()

RCP<const Rational> SymEngine::Rational::neg ( ) const

inline

Returns

negative of this

Definition at line 92 of file rational.h.

    {
        return make_rcp<const Rational>(-i);
    }

Code

powrat() [1/2]

RCP<const Number> SymEngine::Rational::powrat ( const Integer &  other ) const

inline

Raise Rationals to power other

Parameters

other

power to be raised

Definition at line 193 of file rational.h.

    {
        bool neg = other.is_negative();
        integer_class exp_ = other.as_integer_class();
        if (neg)
            exp_ = -exp_;
        if (not mp_fits_ulong_p(exp_))
            throw SymEngineException("powrat: 'exp' does not fit ulong.");
        unsigned long exp = mp_get_ui(exp_);
 
#if SYMENGINE_INTEGER_CLASS == SYMENGINE_BOOSTMP
        // boost::multiprecision::cpp_rational doesn't provide
        // non-const references to num and den
        integer_class num;
        integer_class den;
        mp_pow_ui(num, SymEngine::get_num(i), exp);
        mp_pow_ui(den, SymEngine::get_den(i), exp);
        rational_class val(num, den);
#else
        rational_class val;
        mp_pow_ui(SymEngine::get_num(val), SymEngine::get_num(i), exp);
        mp_pow_ui(SymEngine::get_den(val), SymEngine::get_den(i), exp);
#endif
 
        // Since 'this' is in canonical form, so is this**other, so we simply
        // pass val into the constructor directly without canonicalizing:
        if (not neg) {
            return Rational::from_mpq(std::move(val));
        } else {
            return Rational::from_mpq(1 / val);
        }
    }

Code

powrat() [2/2]

RCP< const Basic > SymEngine::Rational::powrat

(

const Rational &

other

)

const

Raise *this to power other

Parameters

other

exponent

Definition at line 189 of file rational.cpp.

{
    return SymEngine::mul(other.rpowrat(*this->get_num()),
                          other.neg()->rpowrat(*this->get_den()));
}

Code

rpowrat()

RCP< const Basic > SymEngine::Rational::rpowrat

(

const Integer &

other

)

const

Reverse powrat Raise 'other' to power *this

Parameters

other

base

Definition at line 195 of file rational.cpp.

{
    if (other.is_one()) {
        return one;
    }
    RCP<const Integer> res;
    if (mp_fits_ulong_p(SymEngine::get_den(i))) {
        unsigned long den = mp_get_ui(SymEngine::get_den(i));
        if (other.is_negative()) {
            RCP<const Integer> neg_other = other.neg();
            if (not other.is_minus_one()
                and i_nth_root(outArg(res), *neg_other, den)) {
                return SymEngine::mul(this->rpowrat(*minus_one),
                                      res->powint(*get_num()));
            }
        } else if (i_nth_root(outArg(res), other, den)) {
            // res == other**(1/den)
            // return res**num
            return res->powint(*get_num());
        }
    }
    integer_class q, r;
    auto num = SymEngine::get_num(i);
    auto den = SymEngine::get_den(i);
 
    mp_fdiv_qr(q, r, num, den);
    // Here we make the exponent postive and a fraction between
    // 0 and 1. We multiply numerator and denominator appropriately
    // to achieve this
    RCP<const Number> coef = other.powint(*integer(q));
    map_basic_basic surd;
 
    if ((other.is_negative()) and den == 2) {
        imulnum(outArg(coef), I);
        // if other.neg() is one, no need to add it to dict
        if (not other.is_minus_one())
            insert(surd, other.neg(),
                   Rational::from_mpq(rational_class(r, den)));
    } else {
        insert(surd, other.rcp_from_this(),
               Rational::from_mpq(rational_class(r, den)));
    }
    return Mul::from_dict(coef, std::move(surd));
}

Code

subrat() [1/2]

RCP<const Number> SymEngine::Rational::subrat ( const Integer &  other ) const

inline

Subtract Rationals

Parameters

other

of type Integer

Definition at line 126 of file rational.h.

    {
        return from_mpq(this->i - other.as_integer_class());
    }

Code

subrat() [2/2]

RCP<const Number> SymEngine::Rational::subrat ( const Rational &  other ) const

inline

Subtract Rationals

Parameters

other

of type Rational

Definition at line 119 of file rational.h.

    {
        return from_mpq(this->i - other.i);
    }

Code

Field Documentation

type_code_id

const TypeID SymEngine::Rational::type_code_id = SYMENGINE_RATIONAL

static

Type_code_id shared by all instances

Definition at line 22 of file rational.h.

---

The documentation for this class was generated from the following files:

• /home/runner/work/symengine/symengine/symengine/rational.h
• /home/runner/work/symengine/symengine/symengine/rational.cpp